We start from the US census data aggregated at the census block-level (the smallest and most homogeneous census subdivisions). Block-level data provide information about racial composition within a block, but we don’t know the actual spatial distribution of people within a block.


The RL method randomly redistributes people from block into monoracial cells. Each cell has only one racial group. Cells have different population density. This process is stochastic – it means that we repeat it multiple-times and as a results we have many realizations of such redistribution.

STEP 3. Creating RL racial ID and RL population density grids

We create two layers:

RL racial ID and RL population density grids can be transformed into RL image - a high-resolution RGB image that provides a visualization of racial pattern within analyzed area.

RL racial ID and RL population density grids serve also as geospatial data used to calculate racial diversity and segregation indices directly from grid.

STEP 4. Quantification of spatio-racial pattern from grid

RL method quantifies spatio-racial pattern using an exposure matrix - a modification of the co-occurrence matrix. The co-occurrence matrix is a two-way table that summarize cell adjaciencies (i.e. how many times purple and yellow cell appear next to each other). In the exposure matrix each pair contributes the value of their average population densities instead of 1.

STEP 5: Quantification of racial diversity and segregation metrics

The exposure matrix is further summarized using two metrics derived from Information Theory - entropy and mutual information.